NCERT Class XI Mathematics - Probability - Solutions
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Question : 35
Total: 54
Check whether the following probabilities P(A) and P(B) are consistently defined.
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Solution:
(i) P(A ∩ B) must be less than or equal to P(A) and P(B)
Since P(A ∩ B) = 0.6 > 0.5 = P(A)
∴ P(A) and P(B) are not defined consistently.
(ii) P(A ∩ B) = P(A) + P(B) – P(A ∪ B) = 0.5 + 0.4 – 0.8 = 0.9 – 0.8 = 0.1
Since P(A ∩ B) = 0.1 < 0.5 = P(A) and P(A ∩ B) = 0.1 < 0.4 = P(B)
Thus, P(A) and P(B) are consistently defined.
Since P(A ∩ B) = 0.6 > 0.5 = P(A)
∴ P(A) and P(B) are not defined consistently.
(ii) P(A ∩ B) = P(A) + P(B) – P(A ∪ B) = 0.5 + 0.4 – 0.8 = 0.9 – 0.8 = 0.1
Since P(A ∩ B) = 0.1 < 0.5 = P(A) and P(A ∩ B) = 0.1 < 0.4 = P(B)
Thus, P(A) and P(B) are consistently defined.
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